1. Field
The present disclosure relates to the field of delta-sigma modulators. In particular, it relates to a continuous time bandpass delta-sigma modulator using LC resonators.
2. Related Art
FIG. 1 shows a schematic representation of a prior art continuous-time bandpass delta-sigma modulator, showing an input 10, a first transconductor G0, a first second-order resonator 11, a second transconductor G2, a second second-order resonator 12, and a quantizer 13. The delta-sigma modulator of FIG. 1 is a fourth-order delta-sigma modulator, due to the presence of the two second-order resonators, which provide a fourth-order transfer function. Usually, also a feedback loop is present, comprising circuitry 14, which will not be discussed here in detail, because not relevant to the present disclosure. Additionally, although FIG. 1 shows a single feedback loop, multiple feedback and/or feed-forward loops can also be provided.
In a delta-sigma modulator, the poles of the feed-forward open loop are also the zeros of the noise transfer function NTF, i.e. the transfer function between the quantizer noise n and the output. Thus, four zeros in the noise transfer function NTF can, for example, be obtained by inserting four poles in the corresponding feed-forward loop. For example, in the diagram of FIG. 1, four poles are present in the feed-forward loop, due to the presence of the two second-order resonators 11 and 12.
The delta-sigma modulator shown in FIG. 1 can use either active resonators or passive resonators. Active resonators are disclosed, for example, in G. Raghavan, J. F. Jensen et al, “Architecture, design, and test of continuous-time tunable intermediate-frequency bandpass delta-sigma modulators,” IEEE J. Solid-State Circuits, vol. 36, pp. 5–13, January 2001.
Passive resonators, such as LC resonators, are shown in FIG. 2. FIG. 2 is similar to the schematic diagram of FIG. 1 and shows a prior art arrangement taken from J. A. Cherry “On the Design of a Fourth-Order Continuous-Time LC Delta-Sigma Modulator for UHF A/D Conversion”, IEEE Transactions on Circuits and Systems—II: Analog and Digital Signal Processing, Vol. 47, No. 6, June 2000.
The arrangement of FIG. 2 shows second-order LC resonators 15 and 16 acting as analog filtering circuits. The first LC resonator 15 has a resonant frequency f1 and the second LC resonator 16 has a resonant frequency f2.
The transfer function for this chain of resonators is found by multiplying each of the elements G0, G1, 15, and 16 in FIG. 2 together, and is shown in Equation (1).
                              H          ⁡                      (            s            )                          =                              G            0                    ⁢                                    sL              1                                                                        s                  2                                ⁢                                  L                  1                                ⁢                                  C                  1                                            +              1                                ⁢                      G            1                    ⁢                                    sL              2                                                                        s                  2                                ⁢                                  L                  2                                ⁢                                  C                  2                                            +              1                                                          Equation        ⁢                                  ⁢                  (          1          )                    
The input 10 is usually a voltage analog input. The output of the transconductor G0 is a current signal which is input into the LC resonator 15 and output as a voltage signal 17. Also the second LC resonator 16 has a current input and a voltage output. Therefore, a further transconductor G1 is needed, which converts the voltage signal 17 to a current signal 18. The voltage output 19 of the LC resonator 16 is then input into the analog-to-digital converter or quantizer 11.
The presence of the transconductor G1 introduces noise and distortion in the feed-forward loop. In FIG. 2, n1 and d1 represent noise and distortion terms in G1. These refer back to the input by dividing by the gain to obtain
                              n          ⁡                      (            input            )                          =                                            n              1                                      G              0                                ⁢                                                                      s                  2                                ⁢                                  L                  1                                ⁢                                  C                  1                                            +              1                                      sL              1                                                          Equation        ⁢                                  ⁢                  (          2          )                    
At the resonant frequency
      f    1    =      1                            L          1                ⁢                  C          1                    of the resonator 15, n(input)=0. However, away from this resonance frequency, n(input) is not zero and can affect the performance of the modulator. In particular, if resonator 15 has a resonant frequency f1 and resonator 16 has a resonant frequency
            f      2        =          1                                    L            2                    ⁢                      C            2                                ,the noise at f2 is higher than the noise at f1, as shown in FIG. 3, which shows the spectrum of the output signal power. The portion A of the waveform of FIG. 3 shows the noise floor, while portion B shows the desired output signal. In order to obtain the highest signal-to-noise ratio possible, the noise floor should be kept as low as possible.
In particular, for narrowband applications, n(input) is reduced by the gain of the first LC resonator 15 at the desired frequency. However, as the bandwidth increases, to achieve optimal signal-to-noise ratio SNR over a bandwidth, the resonator poles are split apart. As a consequence, the noise of the second, third, etc. resonators is no longer reduces by the same degree because the following resonator poles are located at a different location than the first resonator pole.